Elliptic curves in class 16.2-b over 4.4.13068.1
Isogeny class 16.2-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 16.2-b1
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 7 a^{3} - 13 a^{2} - 69 a - 32\) , \( 32 a^{3} + 13 a^{2} - 124 a - 72\bigr] \)
|
| 16.2-b2
| \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{2} - 2 a - 3\) , \( -33 a^{3} - 45 a^{2} + 15 a - 11\) , \( -427 a^{3} - 825 a^{2} - 21 a + 117\bigr] \)
|
| 16.2-b3
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( -14 a^{3} + 13 a^{2} + 69 a + 8\) , \( a^{3} + 13 a^{2} + 7 a - 18\bigr] \)
|
| 16.2-b4
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 6 a\) , \( 18 a^{3} + 24 a^{2} - 16 a - 1\) , \( -6 a^{3} - 22 a^{2} - 16 a + 7\bigr] \)
|
| 16.2-b5
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a - 1\bigr] \)
|
| 16.2-b6
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 6 a\) , \( 6 a^{3} - 12 a^{2} - 34 a + 11\) , \( 26 a^{3} - 32 a^{2} - 120 a + 41\bigr] \)
|
| 16.2-b7
| \( \bigl[a + 1\) , \( a^{2} - 3 a - 2\) , \( a + 1\) , \( 4 a^{3} + 2 a^{2} - 38 a - 23\) , \( -30 a^{3} + 36 a^{2} + 147 a + 61\bigr] \)
|
| 16.2-b8
| \( \bigl[a + 1\) , \( a^{2} - 3 a - 2\) , \( a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( -a^{3} + a^{2} + 5 a\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 12 & 4 & 2 \\
3 & 1 & 12 & 4 & 2 & 4 & 12 & 6 \\
4 & 12 & 1 & 3 & 6 & 12 & 4 & 2 \\
12 & 4 & 3 & 1 & 2 & 4 & 12 & 6 \\
6 & 2 & 6 & 2 & 1 & 2 & 6 & 3 \\
12 & 4 & 12 & 4 & 2 & 1 & 3 & 6 \\
4 & 12 & 4 & 12 & 6 & 3 & 1 & 2 \\
2 & 6 & 2 & 6 & 3 & 6 & 2 & 1
\end{array}\right)\)
